C150 INSTRUCTOR AND STUDENT HEARD THE LNDG C172 ANNOUNCE CLR OF THE RWY WHEN THEY WERE NOT. THE C150 TOOK OFF OVER THE C172; WHICH WAS ON TXWY AT END OF RWY BUT NOT YET PAST THE HOLD LINE.

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I WAS GIVING DUAL INSTRUCTION TO A STUDENT PLT. WE WERE IN THE RUN-UP AREA TO RWY 31 DOING THE BEFORE CHK. THE CHK WAS COMPLETED AND I WATCHED A C172 LAND ON RWY 31. MY STUDENT DID A 360 DEG CLRING TURN IN THE RUN-UP AREA AND WE CHKED THE PATTERN TO TAKE THE RWY. DURING THE CLRING TURN; I HEARD THE LNDG CESSNA PLT SAY HE WAS CLR OF THE RWY. THE AREA WAS CLR FOR US TO TAKE RWY 31. I LOOKED DOWN THE RWY AND SAW THE CESSNA TURNING ONTO THE PERPENDICULAR TXWY. IT APPEARED TO ME THAT HE WAS CLR OF THE RWY. MY STUDENT TOOK OFF; AND DURING CLBOUT; I LOOKED DOWN AND SAW THAT THE CESSNA THAT JUST LANDED WAS NOT COMPLETELY PAST THE HOLD BARS FOR THE RWY. THERE WAS NOT A COLLISION HAZARD NOR WAS EVASIVE ACTION TAKEN. THINKING BACK; I SHOULD HAVE WAITED A LITTLE LONGER AND WAITED UNTIL THE ACFT WAS FURTHER ONTO THE TXWY; AND NOT ASSUME HE WAS CLR OF THE RWY JUST BECAUSE THE PLT SAID HE WAS. ALSO; THERE ARE ONLY PAINTED HOLD BARS FOR THE RWY AND NO SIGNS FOR THE HOLD BARS. IF SIGNS WERE POSTED; IT WOULD BE EASIER TO KNOW FOR SURE WHEN ANOTHER ACFT HAS CLRED THE HOLD BARS.